Quantum-classical correspondence of a system of interacting bosons in a triple-well potential

E. R. Castro1,2, Jorge Chávez-Carlos3, I. Roditi2, Lea F. Santos4, and Jorge G. Hirsch5

1Instituto de Física da UFRGS Av. Bento Gonçalves 9500, Porto Alegre, RS, Brazil
2Centro Brasileiro de Pesquisas Físicas/MCTI, 22290-180, Rio de Janeiro, RJ, Brazil
3Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México, Cuernavaca, Morelos 62210, México
4Department of Physics, Yeshiva University, New York, New York 10016, USA
5Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apdo. Postal 70-543, C.P. 04510 Cd. Mx., México

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We study the quantum-classical correspondence of an experimentally accessible system of interacting bosons in a tilted triple-well potential. With the semiclassical analysis, we get a better understanding of the different phases of the quantum system and how they could be used for quantum information science. In the integrable limits, our analysis of the stationary points of the semiclassical Hamiltonian reveals critical points associated with second-order quantum phase transitions. In the nonintegrable domain, the system exhibits crossovers. Depending on the parameters and quantities, the quantum-classical correspondence holds for very few bosons. In some parameter regions, the ground state is robust (highly sensitive) to changes in the interaction strength (tilt amplitude), which may be of use for quantum information protocols (quantum sensing).

Studies of the quantum-classical correspondence provide insights into the properties of both the quantum system and its classical counterpart. In this work, we explore the quantum-classical correspondence to locate the quantum phase transition points of an experimentally accessible system of interacting bosons in a triple-well potential. With the semiclassical analysis, we get a better understanding of the different phases of the quantum system and how they could be used for quantum information science.

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[1] M. L. Mehta, Random Matrices (Elsevier Academic Press, Amsterdam, 2004).

[2] G. Casati, F. Valz-Gris, and I. Guarneri, On the connection between quantization of nonintegrable systems and statistical theory of spectra, Lett. Nuov. Cim. 28, 279 (1980).

[3] O. Bohigas, M. Giannoni, and C. Schmit, Spectral fluctuations of classically chaotic quantum systems, Lecture Notes in Physics 263, 18 (1986).

[4] E. B. Rozenbaum, S. Ganeshan, and V. Galitski, Lyapunov Exponent and Out-of-Time-Ordered Correlator's Growth Rate in a Chaotic System, Phys. Rev. Lett. 118, 086801 (2017).

[5] J. Chávez-Carlos, B. López-del Carpio, M. A. Bastarrachea-Magnani, P. Stránský, S. Lerma-Hernández, L. F. Santos, and J. G. Hirsch, Quantum and classical Lyapunov exponents in atom-field interaction systems, Phys. Rev. Lett. 122, 024101 (2019).

[6] S. Pappalardi, A. Russomanno, B. Žunkovič, F. Iemini, A. Silva, and R. Fazio, Scrambling and entanglement spreading in long-range spin chains, Phys. Rev. B 98, 134303 (2018).

[7] S. Pilatowsky-Cameo, J. Chávez-Carlos, M. A. Bastarrachea-Magnani, P. Stránský, S. Lerma-Hernández, L. F. Santos, and J. G. Hirsch, Positive quantum Lyapunov exponents in experimental systems with a regular classical limit, Phys. Rev. E 101, 010202(R) (2020).

[8] Q. Hummel, B. Geiger, J. D. Urbina, and K. Richter, Reversible Quantum Information Spreading in Many-Body Systems near Criticality, Phys. Rev. Lett. 123, 160401 (2019).

[9] T. Xu, T. Scaffidi, and X. Cao, Does Scrambling Equal Chaos?, Phys. Rev. Lett. 124, 140602 (2020).

[10] K. Hashimoto, K.-B. Huh, K.-Y. Kim, and R. Watanabe, Exponential growth of out-of-time-order correlator without chaos: inverted harmonic oscillator, J. High Energ. Phys. 2020 (11), 68.

[11] E. J. Heller, Bound-State Eigenfunctions of Classically Chaotic Hamiltonian Systems: Scars of Periodic Orbits, Phys. Rev. Lett. 53, 1515 (1984).

[12] H.-J. Stöckmann, Quantum Chaos: an introduction (Cambridge University Press, Cambridge, UK, 2006).

[13] D. Villaseñor, S. Pilatowsky-Cameo, M. A. Bastarrachea-Magnani, S. Lerma-Hernández, L. F. Santos, and J. G. Hirsch, Quantum vs classical dynamics in a spin-boson system:manifestations of spectral correlations and scarring, New J. Phys. 22, 063036 (2020).

[14] S. Pilatowsky-Cameo, D. Villaseñor, M. A. Bastarrachea-Magnani, S. Lerma-Hernández, L. F. Santos, and J. G. Hirsch, Ubiquitous quantum scarring does not prevent ergodicity, Nat. Comm. 12, 852 (2021).

[15] K. Nemoto, C. A. Holmes, G. J. Milburn, and W. J. Munro, Quantum dynamics of three coupled atomic Bose-Einstein condensates, Phys. Rev. A 63, 013604 (2000).

[16] B. Liu, L.-B. Fu, S.-P. Yang, and J. Liu, Josephson oscillation and transition to self-trapping for Bose-Einstein condensates in a triple-well trap, Phys. Rev. A 75, 033601 (2007).

[17] P. Buonsante, R. Franzosi, and V. Penna, Control of unstable macroscopic oscillations in the dynamics of three coupled Bose condensates, J. Phys. A 42, 285307 (2009).

[18] T. F. Viscondi, K. Furuya, and M. C. de Oliveira, Phase transition, entanglement and squeezing in a triple-well condensate, EPL (Europhys. Lett.) 90, 10014 (2010).

[19] A. I. Streltsov, K. Sakmann, O. E. Alon, and L. S. Cederbaum, Accurate multi-boson long-time dynamics in triple-well periodic traps, Phys. Rev. A 83, 043604 (2011).

[20] T. F. Viscondi and K. Furuya, Dynamics of a Bose–Einstein condensate in a symmetric triple-well trap, J. Phys. A 44, 175301 (2011).

[21] L. Cao, I. Brouzos, S. Zöllner, and P. Schmelcher, Interaction-driven interband tunneling of bosons in the triple well, New J. Phys. 13, 033032 (2011).

[22] C. J. Bradly, M. Rab, A. D. Greentree, and A. M. Martin, Coherent tunneling via adiabatic passage in a three-well Bose-Hubbard system, Phys. Rev. A 85, 053609 (2012).

[23] Z. Zhou, W. Hai, Q. Xie, and J. Tan, Second-order tunneling of two interacting bosons in a driven triple well, New J. Phys. 15, 123020 (2013).

[24] Q. Guo, X. Chen, and B. Wu, Tunneling dynamics and band structures of three weakly coupled Bose-Einstein condensates, Opt. Express 22, 19219 (2014).

[25] M. K. Olsen, Quantum dynamics and entanglement in coherent transport of atomic population, J. Phys. B 47, 095301 (2014).

[26] G. M. Koutentakis, S. I. Mistakidis, and P. Schmelcher, Quench-induced resonant tunneling mechanisms of bosons in an optical lattice with harmonic confinement, Phys. Rev. A 95, 013617 (2017).

[27] L. Guo, L. Du, C. Yin, Y. Zhang, and S. Chen, Dynamical evolutions in non-hermitian triple-well systems with a complex potential, Phys. Rev. A 97, 032109 (2018).

[28] S. Bera, R. Roy, A. Gammal, B. Chakrabarti, and B. Chatterjee, Probing relaxation dynamics of a few strongly correlated bosons in a 1D triple well optical lattice, J. Phys. B 52, 215303 (2019).

[29] S. Dutta, M. C. Tsatsos, S. Basu, and A. U. J. Lode, Management of the correlations of UltracoldBosons in triple wells, New J. Phys. 21, 053044 (2019).

[30] G. McCormack, R. Nath, and W. Li, Nonlinear dynamics of Rydberg-dressed Bose-Einstein condensates in a triple-well potential, Phys. Rev. A 102, 063329 (2020).

[31] Sayak Ray, Doron Cohen, and Amichay Vardi, Chaos-induced breakdown of Bose-Hubbard modeling, Phys. Rev. A 101, 013624 (2020).

[32] Bo Xiong, and Uwe W. Fischer, Interaction-induced coherence among polar bosons stored in triple-well potentials, Phys. Rev. A 88, 063608 (2013).

[33] V. Penna, and A. Richaud, The phase-separation mechanism of a binary mixture in a ring trimer, Sci Rep 8, 10242 (2018).

[34] A. Richaud, and V. Penna, Phase separation can be stronger than chaos, New J. Phys. 20, 105008 (2018).

[35] T. Lahaye, T. Pfau, and L. Santos, Mesoscopic Ensembles of Polar Bosons in Triple-Well Potentials, Phys. Rev. Lett. 104, 170404 (2010).

[36] D. Peter, K. Pawłowski, T. Pfau, and K. Rzażewski, Mean-field description of dipolar bosons in triple-well potentials, J. Phys. B 45, 225302 (2012).

[37] A.-X. Zhang and J.-K. Xue, Dipolar-induced interplay between inter-level physics and macroscopic phase transitions in triple-well potentials, J. Phys. B 45, 145305 (2012).

[38] L. Dell'Anna, G. Mazzarella, V. Penna, and L. Salasnich, Entanglement entropy and macroscopic quantum states with dipolar bosons in a triple-well potential, Phys. Rev. A 87, 053620 (2013).

[39] L. H. Ymai, A. P. Tonel, A. Foerster, and J. Links, Quantum integrable multi-well tunneling models, J. Phys. A 50, 264001 (2017).

[40] K. W. Wilsmann, L. H. Ymai, A. P. Tonel, J. Links, and A. Foerster, Control of tunneling in an atomtronic switching device, Comm. Phys. 1 (2018).

[41] A. P. Tonel, L. H. Ymai, K. W. Wilsmann, A. Foerster, and J. Links, Entangled states of dipolar bosons generated in a triple-well potential, SciPost Phys. 12, 003 (2020).

[42] D. Blume, Jumping from two and three particles to infinitely many, Physics 3, 74 (2010).

[43] D. Blume, Few-body physics with ultracold atomic and molecular systems in traps, Rep. Prog. Phys. 75, 046401 (2012).

[44] A. Dehkharghani, A. Volosniev, J. Lindgren, J. Rotureau, C. Forssén, D. Fedorov, A. Jensen, and N. Zinner, Quantum magnetism in strongly interacting one-dimensional spinor Bose systems, Sci. Rep. 5, 1 (2015).

[45] Zinner, Nikolaj Thomas, Exploring the few- to many-body crossover using cold atoms in one dimension, EPJ Web of Conferences 113, 01002 (2016).

[46] M. Schiulaz, M. Távora, and L. F. Santos, From few- to many-body quantum systems, Quantum Sci. Technol. 3, 044006 (2018).

[47] T. Sowiński and M. Á. García-March, One-dimensional mixtures of several ultracold atoms: a review, Rep. Progr. Phys. 82, 104401 (2019).

[48] G. Zisling, L. F. Santos, and Y. B. Lev, How many particles make up a chaotic many-body quantum system?, SciPost Phys. 10, 88 (2021).

[49] T. Fogarty, M. A. Garcia-March, L. F. Santos, and N. L. Harshman, Probing the edge between integrability and quantum chaos in interacting few-atom systems, Quantum 5, 486 (2021).

[50] F. Serwane, G. Zürn, T. Lompe, T. Ottenstein, A. Wenz, and S. Jochim, Deterministic preparation of a tunable few-fermion system, Science 332, 336 (2011).

[51] A. N. Wenz, G. Zürn, S. Murmann, I. Brouzos, T. Lompe, and S. Jochim, From Few to Many: Observing the Formation of a Fermi Sea One Atom at a Time, Science 342, 457 (2013).

[52] Codes and data shall be provided upon request.

[53] K. Hepp, The Classical Limit for Quantum Mechanical Correlation functions, Commun. Math. Phys. 35, 265 (1974).

[54] A. J. Leggett, Bose-Einstein condensation in the alkali gases: some fundamental concepts., Rev. Mod. Phys. 73, 307 (2001).

[55] O. Castaños, R. Lopez-Peña, and J. G. Hirsch, Classical and quantum phase transitions in the Lipkin-Meshkov-Glick model, Phys. Rev. B 74, 104118 (2006).

[56] C. L. Degen, F. Reinhard, and P. Capellaro, Quantum sensing, Rev. Mod. Phys. 89, 035002 (2017).

[57] D. S. Grun, Leandro. H. Ymai, K. W. Wittmann, A. P. Ymai, and Angela Foerster, Jon Links, Integrable atomtronic interferometry, (2020), arXiv:2004.11987 [quant-ph].

[58] D. S. Grun, K. W. Wittmann, Leandro. H. Ymai, Jon Links, and Angela Foerster, Atomtronic protocol designs for NOON states, (2021), arXiv:2102.02944 [quant-ph].

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[4] Goran Nakerst and Masudul Haque, "Chaos in the three-site Bose-Hubbard model: Classical versus quantum", Physical Review E 107 2, 024210 (2023).

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[6] Tianyi Yan, Matthew Collins, Rejish Nath, and Weibin Li, "Signatures of Quantum Chaos of Rydberg-Dressed Bosons in a Triple-Well Potential", Atoms 11 6, 89 (2023).

[7] K. Wittmann W., L. H. Ymai, B. H. C. Barros, J. Links, and A. Foerster, "Controlling entanglement in a triple-well system of dipolar atoms", Physical Review A 108 3, 033313 (2023).

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